What is interesting about such a definition is that it can be easily generalized to the representations of other algebras, which makes them applicable to other physical theories such as chromodynamics, where \(SU(3)\)  group should be used. In this case representations should be enumerated not by natural numbers as in \(SU(2)\)  case, but by Young diagrams \(T=[T_1,\ldots T_n]\) , \(T_1\ge T_2 \ge T_3 \ldots \) . However, one can generalize this definition to not only other Lie algebras, but also to their deformations such as quantum groups [1]}. Quantum groups are essentially a deformation of universal enveloping algebras. They are connected among other things integrable systems [2]}, lattice gauge theory [3]}, 3-d quantum gravity [4]}, quantum \(sl_N\)  invariants of knots [5]}, Turaev-Viro invariants of 3-manifolds and topological field theory [6]}, [7]}, WZW conformal field theory and 3d Chern-Simons theory [8]}, [9]}. In the latter case quantum groups describe the hidden symmetries of the observables, which are also equal to the knot polynomials from the knot theory.
